On the complexity of quantum link prediction in complex networks

João P. Moutinho, Duarte Magano, Bruno Coutinho

Published 2022-11-29Version 1

Link prediction methods use patterns in known network data to infer which connections may be missing. Previous work has shown that continuous-time quantum walks can be used to represent path-based link prediction, which we further study here to develop a more optimized quantum algorithm. Using a sampling framework for link prediction, we analyse the the query access to the input network required to produce a certain number of prediction samples. Considering both well-known classical path-based algorithms using powers of the adjacency matrix as well as our proposed quantum algorithm for path-based link prediction, we argue that there is a polynomial quantum advantage on the dependence on $N$, the number of nodes in the network. We further argue that the quantum complexity of our quantum link prediction algorithm, although sub-linear in $N$, is limited by the complexity of performing a quantum simulation of the network's adjacency matrix, which may prove to be an important problem in the development of quantum algorithms for network science in general.